Equivalence and self-improvement of p-fatness and Hardy's inequality, and association with uniform perfectness

Riikka Korte*, Nageswari Shanmugalingam

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

9 Citations (Scopus)

Abstract

We present an easy proof that p-Hardy's inequality implies uniform p-fatness of the boundary when p = n. The proof works also in metric space setting and demonstrates the self-improving phenomenon of the p-fatness. We also explore the relationship between p-fatness, p-Hardy inequality, and the uniform perfectness for all p ≥ 1, and demonstrate that in the Ahlfors Q-regular metric measure space setting with p = Q, these three properties are equivalent. When p ≠ 2, our results are new even in the Euclidean setting.

Original languageEnglish
Pages (from-to)99-110
Number of pages12
JournalMATHEMATISCHE ZEITSCHRIFT
Volume264
Issue number1
DOIs
Publication statusPublished - Jan 2010
MoE publication typeA1 Journal article-refereed

Keywords

  • Hardy's inequality
  • Metric spaces
  • Self-improvement
  • Uniform p-fatness
  • Uniform perfectness

Fingerprint Dive into the research topics of 'Equivalence and self-improvement of p-fatness and Hardy's inequality, and association with uniform perfectness'. Together they form a unique fingerprint.

Cite this